I am a newbie and a future audiophile. I have a question about my first loudspeaker from last year. This MS-paint picture shows how it was set up.

When we connected the two ends of the magnet-wire to my friend's stereo system, lo and behold, the coil induced a magnetic field, which interacted with the permanent magnetic field and the cone vibrated producing sound.

(Sorry if that was long-winded and unnecessary. As a newbie, I am happy that I'm finally understanding this stuff.)

My friend's amplifier had ports in the back to connect to speakers using magnet wire, but I don't have one of these systems. I would like this speaker to play sound from my mp3 player.

What kind of adapter do I need to connect the two ends of this magnet-wire to a 1/8" headphone jack?

I have looked and looked, but I haven't found any adapters that look like they could connect my speaker to an mp3 player.

I realize that I will also need an amplifier, but I think (I hope) I can build one. My question is how to use this speaker with an mp3 player. Any advice is much appreciated.

The output of the headphone jack on an MP3 player does not generate enough current to drive anything but the tiny speakers in earphones. I cannot tell from your post if your speaker is home made or experimental. If so it is probably very inefficient. You will need an amplifier to drive any kind of speaker. Maybe you are experimenting but if not and you just want a cheap solution to hook to your MP3 player just get some inexpensive amplified computer speakers and plug them into your MP3 player. Some can be had for a few dollars and they have a small amplifier built in.